In recent years, the use of magnesium alloys in sheet metal forming has been taken notice by many researchers due to low density and high strength. Because of low formability of magnesium alloy in room temperature, warm forming has been developed in order to produce parts of magnesium alloy sheet. In this paper, warm deep drawing process of circular cup from magnesium alloy AZ31B sheet was simulated using the finite element software ABAQUS/Standard. Simulation results obtained from this study agreed well with experimental results and show that the limit drawing ratio increases with increase in the forming temperature. Maximum LDR was obtained 2.5 at the forming temperature of 200°C. Simulation results indicate that heat transfer plays an important role in increase formability. By comparing isothermal warm deep drawing with non-isothermal one, heat transfer effect and location of sheet failure have been investigated. The effects of friction coefficient and punch speed on the limit drawing ratio were also studied. As a result, increase in the friction coefficient leads to increase in the punch force and decrease in the limit drawing ratio. Results also show that the maximum friction coefficient to produce acceptable parts increase with increase in the forming temperature. In addition, results indicate that increase in the punch speed leads to decrease in the limit drawing ratio.